I’m generally amused/irritated with discussions of streaks, hot hands, bad starts, and other events. Statistically, this doesn’t really make any sense. One of the great books I’ve read recently on the subject was specifically aimed at sports and called “Scorecasting” (recommended from someone on this blog, I might add—thank you).
This is particularly acute with the recent road trip and poor, lambasted Felton and beleaguered McMillan.
Let’s see if we can put this in a way that can help reveal the lie of our intuition disguising the mathematical realities.
We’re all familiar with streaks on the roulette table or games of Risk. This leads to the “gambler’s fallacy” that has been discussed at length elsewhere on this website. But let’s apply it to sports.
Let’s assume a hypothetical LaMarcus Aldridge. We’ll call him Excel Aldridge. Let’s further assume that he’s shooting a pure 45% from the field: every single shot he takes has a 45% chance of scoring. We could assume that he takes a pure 30 shots a game but let’s insert another bit of randomness—let’s assume that each shot only has a 70% chance of being “born” because of offensive vagaries, defensive pressure, or whatever. Let’s finally assume that LMA gives 100% effort every single play so his shooting percentage never deviates and he takes every shot the offense gives him.
Statistically, this would mean LMA would take 21 shots every game, scoring 18.9 points—throw in some number of free throws and you have an easy all-star level player.
Finally, let’s assume a hypothetical hysterical beat reporter named Jeffrey Nimble. How might the first series of games gone down? Let’s let MS Excel throw spit out some random numbers and see:
Game 1: Aldridge is off to a bad start to the season scoring 16 points but needing 25 shots to do it. He missed his first 3 shots and eventually missing 11 of his first 13. McMillan doggedly kept feeding the post and Aldridge turned it around in the second half. 8/25 for 32% shooting percentage.
Game 2: Aldridge rebounds the next night with a workmanlike 22 point outing in game 2, going 4 of 6 to start the game and drilling the opponent at the end of the game with four straight makes in crunch time when it mattered most. 11/23 for 48% shooting percentage.
Game 3: Aldridge’s struggle with his shooting return even though he scored 18 points. Late in the second half he faded missing 5 of his last 6 shots including all 4 close end the game. 9/25 for 36%
Game 4: Aldridge dominates at last with a 28pt outburst controlling the paint all night. He was consistent with his shot all game long finishing 14/28 for a pure 50%. This is exactly what the Blazers need him to do every night.
Game 5: Aldridge finishes the game with an average-for-him 20 points. He started out hot in the first half hitting all five of his first shots. But once again we see him fading—possibly due to the condensed schedule and the back-to-back night—at one point missing 9 straight shots and showing visible frustration. 10/24 for 42% from the field.
This is me forcing a fictional narrative on to absolute random chance according to MS Excel’s random number generator. Just like we predicted, Excel LMA is averaging 20.8 points per game and shooting 48% from the field. But in that stretch he two occasions of 8+ misses in a row. Reading into mathematical fiction like this is like lazy reporting from a box score and hardly enlightening.
Why go through this exercise? Sports is a pursuit where we’re attaching a narrative to statistical probability and this is fun—just like gambling is fun—but it’s fraught with errors in judgment. Understanding the difference between a perfectly normal streak and a developing penchant for turnovers or a developing accuracy in 3 point shooting is a big problem. It’s a place where I try to give the benefit of the doubt to the coaching staff. We see Nolan take maybe 3 shots in a game. That’s way too small a size to make a judgment. Nate sees Nolan take hundreds of shots in practice—he has a much better read.
What I have come to do is respect offenses and systems. Are the Blazers getting open shots? Are they getting shots in motion? Shots off assists? Or are they taking flaming bag shots or isolation shots? I love seeing our defensive and offensive systems work because those systems are generating better statistical probabilities. This is good coaching.
I am not alarmed when a good shooter misses several in a row if they’re good shots. Is he resilient? Does he let it affect him? Do a few misses rattle him? These are the danger signs. Good players, I think, instinctively understand this… fans would have a lot less heartache if they did too. Good coaching creates players who do not get down on themselves when streaks develop.
Does Nate meet these two criteria? Yes, I think he does.